Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT175 °C40 °C110 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 40 °C while the cold fluid heats from 15 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 40 °CTc: 15 → 110 °C
ΔTlm = K
2.Easy
lengthT100 °C75 °C55 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 6 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 100 to 75 °C and the cold fluid heats from 10 to 55 °C. Find the heat transfer rate Q̇.

A = 6 m²U = 1000 W/(m²·K)Th: 100 → 75 °CTc: 10 → 55 °C
Q̇ = kW
3.Medium
lengthT140 °C25 °C125 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 125 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 125 °CU = 2000 W/(m²·K)
A = m²
4.Medium
lengthT80 °C30 °C35 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 380 kW. The hot fluid cools from 80 to 30 °C and the cold fluid heats from 10 to 35 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 380 kWU = 800 W/(m²·K)Th: 80 → 30 °CTc: 10 → 35 °C
A = m²
5.Hard
lengthT130 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 2 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 2 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT105 °C70 °C28.79 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 105 to 70 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 105 → 70 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 41.86 K
  2. 2. Q̇ = 326.3 kW
  3. 3. A = 2.129 m²
  4. 4. A = 15.41 m²
  5. 5. Tc,out = 78.77 °C
  6. 6. A = 2.216 m²

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